StarPlot Documentation

1. Introduction to Stellar Astronomy

This section is a crash course in basic stellar astronomy, written
so that even people without a background in the subject can
use StarPlot and understand the display. If you already
have some knowledge in the field, feel free to skip this section.

1.1. Coordinate Systems

The first thing an astronomer needs to know about an object in the
sky is where to find it. Most commonly this information comes in
the form of a right ascension (RA) and declination.
These are two angular coordinates, similar respectively to the
longitude and latitude of a point on the Earth's surface. One can
imagine a sphere centered on the Earth, whose radius is larger than
that of the known universe. This fictitious sphere is called the
celestial sphere. The RA and declination of an object are
defined as the coordinates of the point on the celestial sphere onto
which the object is projected, as seen from the Earth.

For convenience, the north and south poles of the celestial sphere's
coordinate system are aligned with those of the Earth. In other words,
if one stands at the Earth's north pole, the north pole of the
celestial sphere is directly overhead. This almost coincides with the
projection of the star Alpha Ursae Minoris onto the celestial sphere;
hence that star has a declination of almost 90° N, and we call it
the North Star, or Polaris.
(Declination, like latitude, is measured in degrees, minutes and
seconds of arc.) More generally, an object in the sky with declination
d will pass overhead at some point during the day or night as
seen from a point on Earth with latitude d.

Right ascension is more complicated, because the Earth rotates while
the rest of the universe, as a whole, does not. So astronomers can't
use Earthly longitudes to determine celestial right ascensions in the
same way that they do with latitudes and declinations. Instead, they
define a specific direction in the sky to be the zero meridian.
This point, called the first point of Aries (FPA), is the place
where the Sun's projection onto the celestial sphere crosses the
celestial equator at the beginning of spring. (It happens to lie
in the constellation of Aries, the Ram; hence the name.)

Now, suppose the FPA happens to be directly
above the Earth's southern horizon, as seen from somewhere in the
northern hemisphere. As the Earth rotates, this point on the
celestial sphere will appear to set in the west. After a time period
called a sidereal day, the FPA will have risen
again in the east and once again be directly above the southern
horizon. A sidereal day is slightly shorter than a solar day, roughly
23 hours and 56 minutes. (This is because the Earth, in its orbit
around the Sun, makes one additional rotation per year if considered
relative to the distant stars than if considered relative to the Sun.)

A sidereal day may be divided into 24 periods called sidereal hours,
each slightly shorter than a standard hour. If the current
sidereal time is h (the number of sidereal hours since the
FPA was last due south), then the points which are
now directly over the southern horizon are said to have right ascension
h. For instance, after the FPA is due south, one must wait
6 sidereal hours and 43 sidereal minutes before the star Sirius is
directly over the southern horizon. Therefore the right ascension
of Sirius is 6 hrs 43 min. Looking due south from a point in the
northern hemisphere, right ascension increases going from right
to left.

As an aside, notice that one hour of right ascension is equivalent
to 360° / 24 = 15° of longitude. It is unfortunate that an
hour of right ascension is divided into 60 minutes or 3600 seconds of
right ascension, because these units have nothing to do with the
similarly named minutes and seconds of arc into which the degrees of
latitude or declination are divided.

This is probably all very confusing, so I will summarize quickly:
An object in the sky located at right ascension h and
declination d will pass directly overhead as seen by an
observer located at Earthly latitude d when the local
sidereal time is h. Local sidereal time is dependent upon
both the current solar time and the day of the year. In general, the
sidereal time h (in sidereal hours) equals ( t
+ 24f ) mod 24,
where t is the local solar time (in standard hours), and
f is the fraction of a year which has passed since the last
vernal equinox.

The above-described coordinate system is called
celestial coordinates. Given the celestial coordinates of
an object in the sky, it is nearly trivial to determine where the
best place on Earth is from which to observe the object, at what time
the object will be highest above the horizon on a given date, and how
high it will be at that time. For this pragmatic reason, the celestial
coordinate system is the most often-used.

However, astronomers also frequently use a different system called
galactic coordinates. This system uses the plane of our
Milky Way Galaxy, projected onto the celestial sphere, as its equator.
The galactic latitude of an object is therefore given by its angular
distance from the plane of the Milky Way, as seen from Earth. Galactic
longitude is given using meridians perpendicular to the galactic plane,
with meridian zero defined as the direction to the center of the Milky
Way. In this system, both latitude and longitude are measured in
degrees, just like Earth-based latitude and longitude (except there are
no "east" or "west" longitudes; galactic longitude starts at zero and
increases in the counterclockwise direction until it reaches 360°).

Although galactic coordinates are not simply related to an object's
position in the sky as celestial coordinates are, they have the
advantage of being more meaningful and less Earth-centric. The
knowledge that a distant star has a high galactic latitude, for
example, suggests it is one of the old halo stars rather than a new
star within the galactic disk. Objects outside our galaxy are
typically easier to see if they have a high galactic latitude because
less gas and dust is in front of them from our viewpoint.

The conversion between galactic and celestial coordinate systems
involves a great deal of irritating trigonometry. StarPlot supports
both coordinate systems, and allows you to switch easily between them
without hassle.

1.2. Distances and Parallax

So far we have only considered two of the three variables necessary
to specify a star's three-dimensional location in space. The third
variable, of course, is distance from Earth. Unlike a star's
apparent position on the celestial sphere, however, its distance
is difficult to determine. In general two methods are available:
using a star's trigonometric parallax, and estimating its
distance from its spectral lines and apparent brightness.

By far the more accurate of these is the parallax. Over a period of
six months, the Earth travels in its orbit from one side of the Sun
to the other, a shift in position of about 300 million kilometers.
Parallax is simply one-half the angle by which a distant star appears
(to us) to shift position on the celestial sphere due to this motion.
The more distant the star, the smaller its parallax. The nearest star
excepting our Sun, Proxima Centauri, has a parallax of 0.78 seconds of
arc. Recall that a second of arc is 1/3600 of a degree, which itself
is 1/360 of a full circle. Stars are exceedingly far away.

Astronomers prefer to measure stellar distances with a unit called
the parsec (pc). A parsec is defined as the distance at which
a star would have a parallax of one
second of arc, and is
equal to about 31 trillion kilometers. However, another unit of
similar size called the light-year (LY) is more favored in
popular science and science fiction. The light-year is the distance
which a beam of light would take one year to travel in a vacuum.
It is roughly 9.5 trillion kilometers, or 1/3.2616 of a parsec.
Because of the unit's popularity, I have chosen to make the light-year
be the default distance unit in StarPlot. If you prefer parsecs,
you can change this from the Options->Distance Units submenu
in StarPlot versions 0.95.5 and newer.

Unfortunately, we cannot accurately measure parallaxes smaller than
a few hundredths of a second of arc. Hence, stars farther away than
about one or two hundred light-years must have distances determined
via the second method. This will be described later. It is worth
noting that while stellar parallaxes may be off by an order of 10 %,
distances obtained from a star's apparent brightness and spectrum
might easily be wrong by a factor of two.

1.3. Stellar Magnitudes

Other than the positional data described above, the first piece of
information one might want to know about a star is its brightness.
This is described using a logarithmic scale called magnitude.
A star has an apparent magnitude that describes its brightness
as seen from Earth, and also a more objective
absolute magnitude
related to its intrinsic brightness. To avoid confusion, in this
chapter I will use
the adjectives "bright" or "faint" to refer to a star's apparent
brightness, and "luminous" or "dim" to refer to its objective
brightness (luminosity). In the remaining chapters, all of these
adjectives will always refer to a star's objective brightness.

Astronomers define the apparent magnitude m of a star, as seen
from the Earth, to be m =
-2.5 log10r,
where r is the ratio of the star's brightness to that of the
bright star Vega. Notice that (1) fainter stars have larger magnitudes;
(2) if the difference in magnitudes between two stars is 1, then
one is 100.4, or about 2.512, times fainter than the other.
The reason for this logarithmic scale is that ophthalmologists used
to believe that human night vision perceived brightnesses
logarithmically.

The brightest star in the night sky is Sirius, with an apparent
magnitude of -1.46. That is, Sirius is
10(0.4)·(1.46) = 3.8 times brighter than Vega.
(For comparison, the Sun has an apparent magnitude
of -27 or so, and the full moon, -12.) The faintest stars visible
to a human with good eyesight, without optical aid, in a dark area
far from city lights, have apparent magnitudes between +6 and +6.5
(and thus are 1000 to 1500 times fainter than Sirius).
The faintest objects detectable by any human instruments have apparent
magnitudes as large as +29.

The absolute magnitude M of a star is then defined as the
apparent magnitude which that star would have if it were moved to a
distance of 10 parsecs (32.16 light-years) from Earth.
Our Sun is a relatively dim star, having an
absolute magnitude of +4.85. However, stars may be much dimmer;
the vast majority are small, relatively cool, and dimmer than absolute
magnitude +10 or so. On the other hand, exceptionally luminous stars
may have absolute magnitudes in the range of -5 or -6.

Knowing a star's absolute and apparent magnitudes, one may use the
formula D =
(10 pc)·10(m-M)/5 to
calculate its distance D in parsecs. This allows for the
second method of distance determination listed earlier, because
often one can estimate a star's absolute magnitude from knowledge
of the lines in its spectrum.

1.4. Spectral Classes

A star's spectrum can provide a great deal of useful information about
it, including but not limited to its temperature, density, speed of
rotation, radial velocity, possible unseen companions, and of course,
composition. Most of these variables affect only the details of
spectra, however. Only the composition and temperature have very
obvious effects. Since most stars have approximately the same
composition in their external layers, usually the only important
variable is the temperature at the surface of the star.

Because temperature is a continuous scalar variable, it is
possible to arrange the major types of stellar spectra in a
one-dimensional sequence. Each type of spectrum has been designated
by a letter, called the Harvard spectral type. From hottest to
coolest, the major spectral types are O, B, A, F, G, K and M. (When
this system of types was developed in the 1890's, the effects of
temperature upon stellar spectra were unknown, leading to the somewhat
random-seeming order of these letters.) Type O and B stars are hot and
blue-white, while M stars are cool and appear red. Each spectral type
is subdivided by appending a number in the range [0,10), where a
subtype "0" is hotter than a subtype "9". Our Sun has spectral type
G2, indicating a surface temperature of about 5800 Kelvins
(10,000°F).

Using parallax data, one can make a scatter plot of star absolute
magnitudes versus spectral type (or equivalently, temperature). Such
a graph is known as a Hertzsprung-Russell (H-R) diagram.
Traditionally the diagram is plotted with temperature increasing from
right to left, and luminosity increasing (magnitude decreasing) from
bottom to top. Surprisingly, the stars on such a diagram, rather than
being scattered all over it, lie in several well-defined bands. The
most important contains about 90% of all stars, and extends diagonally
from luminous blue O stars at upper left to dim red M stars at lower
right. This is the main sequence. Bands of stars lying above
the main sequence (having greater luminosities) lie in the
giant and supergiant regions.

The Morgan-Keenan luminosity class is an attempt at a numerical
system for describing these bands. A Roman numeral between I and VI
is added to the end of the spectral type, with I representing
supergiants, II and III giant stars, IV the rare "subgiants," V the
main sequence or "dwarfs," and VI the so-called "subdwarfs." Naturally
this classification is somewhat subjective. Nonetheless, certain
features of a star's spectrum, if examined closely, make it possible to
guess a star's luminosity class without knowing its absolute magnitude.
From the spectral type and luminosity class, one can estimate the
absolute magnitude, and therefore the star's distance as well.

Of course, a small percentage of stars don't fall into these tidy
categories. A class of stars called white dwarfs (not to
be confused with the main sequence "dwarfs" or "subdwarfs") lies to
the bottom left of a Hertzsprung-Russell diagram, combining high
temperatures with surprising dimness. The Wolf-Rayet stars
lie far to the left, and some exotic objects such as pulsars and black
holes don't even have a place on the chart.

1.5. Stellar Evolution

From lengthy observations and inspired hypotheses, astronomers have
arrived at a reasonably good understanding of stellar evolution. Stars
begin "life" via gravitational condensation from clouds of gas and
dust. Thousands of them form in a cluster at once. Once nuclear
fusion has begun in a star's core and it has reached an equilibrium
state, it starts out in the main sequence. More massive stars start
in the upper left corner of the H-R diagram, while less massive ones
begin in the lower right. (The minimum mass required for a star to
reach stable equilibrium with nuclear fusion is about 1/12 the mass
of our Sun.)

During the main sequence, the star "burns" hydrogen, converting it
to nuclei of the isotopes helium-3 and (primarily) helium-4 via
nuclear fusion. In the process, energy (in the form of gamma rays)
is released. The outward radiation pressure from this energy
prevents the star from collapsing. The fusion mechanism is the
proton-proton chain in smaller
stars, a step-by-step process that one might intuitively expect. But
in stars slightly larger than our Sun, the CNO
(carbon-nitrogen-oxygen) cycle predominates. This cycle
uses traces of carbon-12 (left over from earlier generations of
stars) in the star's core to catalyze the hydrogen to helium
conversion.

The more massive a star is, the shorter its lifespan, for the rate
of nuclear reactions is strongly dependent upon the stellar core
temperature, which in turn is a function of pressure. Sunlike stars
may last 10 billion years in the main sequence stage, while stars
starting out at type O on the main sequence will survive for "only"
a few million.

At the end of the main sequence phase, a star's life is nearly over.
The star's core becomes clogged with too much helium for fusion
of hydrogen to continue. At this point, the outward radiation from
fusion will no longer support the mass of the star against gravity.
As pressure rises in the core, so does the temperature. If the
star is large enough, the temperature and pressure will reach a point
at which fusion of three helium nuclei to form a nucleus of carbon-12
can occur. (This is known as the triple-alpha process, since helium-4
nuclei are also called alpha particles.) Smaller stars collapse into
a dense object called a white dwarf.

The intense temperatures in the stellar core cause outer layers of
the star to expand, swelling to tens of millions of kilometers in
diameter. They may engulf planets near the star. As these layers
are now far from the central heat source, they
become cooler and glow a reddish color. This phase of the star's life
is the "red giant" stage.

Eventually, the helium to burn also runs out. Most stars do not
have the mass to induce the next phase of fusion (carbon burning),
and at this point many of them will also collapse into white dwarfs.
On the way to doing so, they may eject enormous spherical clouds of
gas, called planetary nebulae due to their resemblance through a
telescope to a planetary disk.

More massive stars will continue to find more and more exotic things
to "burn," in the process swelling to enormous size. These brilliant
objects are supergiants. They survive until their cores are filled
with iron. Iron, as the most stable of elements (having the greatest
binding energy per nuclear particle) cannot be burned. An iron
nucleus does not release energy, either when fused with other nuclei
or when split apart into smaller pieces. A star in this situation
typically undergoes a supernova, a massive explosion, leaving behind
an exotic neutron star or black hole.

This sketch of stellar evolution is only the briefest outline, and
greatly oversimplifies. For more detail, the reader is suggested
to start with the Wikipedia article
and then follow the references from it.

1.6. Star Names

One large problem astronomers have with stars, since there are
billions of them in our galaxy alone, is naming them. The ancient
Greeks and Arabs simply named the brightest stars individually. Some
of these names, like "Betelgeuse," are still well-known, while others
such as "Zubeneschamali" are barely used anymore. However, this
approach did not scale well, even to the only 6000 stars visible
to the unaided eye.

One of the first systematic naming attempts was made by Johann Bayer
in 1603. He identified the stars in each constellation with a Greek
letter, starting with α (alpha) for the brightest star and
working his way down. This was before the telescope was used in
astronomy, and long before photography or electronic devices, so
often he made mistakes: α Orionis (a.k.a. Betelgeuse) is the
second-brightest star in the constellation Orion. Rather than write
out the entire constellation name all the time, astronomers will use
just the standard three-letter abbreviations; Orionis becomes Ori.
A list of the 88 constellations and their abbreviations can be found
as an appendix in most astronomy handbooks.

As there are only 24 Greek letters, and many more stars than that
in each constellation, Bayer sometimes resorted to superscripts, so
we have (for instance) π1 through π6
Orionis. StarPlot assumes that Greek letters are spelled out,
constellations are abbreviated, and superscripts are represented in
parentheses like this in its ASCII text data files: "Pi(1) Ori". In
the graphical display, StarPlot will convert the Greek letter names
into actual Greek letters, and use superscripts where necessary:
.

Clearly, more star names were needed. Around 1725, the astronomer
John Flamsteed gave stars numbers (which, unlike Greek letters, are in
inexhaustible supply) from west to east in each constellation, in
order of increasing right ascension. In addition to being called Rigel
and Beta Orionis, the brightest star in Orion now became 19 Orionis as
well. One minor problem: Flamsteed never numbered stars which were
too far south to be seen from England. Hence a lot of stars in the
far southern sky which lack Bayer designations are still known by such
constructs as I Carinae or L2 Puppis.

One additional set of star designations uses the constellation names.
Some stars vary cyclically in brightness over time; these are called
variable stars. A German astronomer named F.W.A. Argelander decided
that these stars needed their own system of nomenclature. He
began with the letter R for the brightest variable star in each
constellation, for instance, R Andromedae. (In some constellations,
the letters up through Q were already taken.) After reaching Z, he
started a confusing system of double letters, which finished at QZ with
the 334th variable in a constellation. Rather than continue his mess,
later astronomers decided to name further variables V335, V336, and so
on.

More recently, constellation names have gone out of style in star
naming schemes. In 1859, Argelander also began a massive star catalog
called the Bonner Durchmusterung (Bonn Survey), in which stars
were labeled by position. Rigel, for example, is BD -08°1063,
meaning it is the 1063rd star (counting from 0 hours right ascension)
which was catalogued in the strip of the celestial sphere between
-8° and -9° declination. Two other surveys, which labelled
stars "CD" and "CP," completed coverage of the entire celestial sphere.
These surveys covered over a million stars. Due to the effects of
precession (a slow variation in the direction of the Earth's axis),
though, the declination expressed in a star's BD designation is often
no longer quite the same as its current declination.

In the 1910's and 1920's, the Henry Draper Catalogue (HD) was compiled
as a listing of stellar spectra, containing over 200,000 stars numbered
by increasing right ascension: HD 1 through HD 225300. The Smithsonian
Astronomical Observatory (SAO) released its own catalog of more than
250,000 stars in 1966. Reasonably bright stars (brighter than about
10th magnitude) are almost all covered by one of the catalogs described
here, usually several.

However, astronomers also use many other special-purpose catalogs.
These are especially noticeable in the set of nearby stars, most of
which are dim red dwarfs below the magnitude limit of any catalog
already described. Commonly seen designations in the Gliese data
set (available from the StarPlot web site) include the Gliese, Giclas,
Wolf, Ross, Luyten and LHS catalogs. And some stars, like Barnard's
Star or van Maanen's Star, are simply named after their discoverers.